The SPH equations are described in detail by Liu and Liu [1]}. In this paper, we consider the application of three-dimensional SPH to free surface problems. The SPH method represents continuous fluid using a set of particles. Each particle \(i\)  has physical quantities, such as mass \(m_i\) , position \(\mathbf {r}_i\) , velocity \(\mathbf {v}_i\) , density \(\rho _i\) , and pressure \(P_i\) . Each particle in the SPH method is associated with a support domain. The SPH approximation, which consists of the particle approximation and the kernel approximation, is performed within the current support domain. The value of a function defining a physical quantity can be approximated by its values at a number of neighboring particles. The SPH method uses the concept of integral representation of a field function \(f(x)\)  by the following identity
\(<f(\mathbf {r})> = \int _\Omega f(\mathbf {r^{\prime }})W(|\mathbf {r}-\mathbf {r^{\prime }}|,h)d\mathbf {r^{\prime }},\) 
